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Question

(C) There are two sections,$A$ and $B$,each with $5$ questions. The candidate must select $6$ questions in total,with at least $2$ questions from each

Vedclass · Accepted Answer

$200$

Vedclass · Answer

(C) There are two sections,$A$ and $B$,each with $5$ questions. The candidate must select $6$ questions in total,with at least $2$ questions from each section.The possible cases are:$(i)$ Selecting $2$ questions from section $A$ and $4$ questions from section $B$:$^5C_2 	imes ^5C_4 = 10 	imes 5 = 50$ ways.$(ii)$ Selecting $3$ questions from section $A$ and $3$ questions from section $B$:$^5C_3 	imes ^5C_3 = 10 	imes 10 = 100$ ways.$(iii)$ Selecting $4$ questions from section $A$ and $2$ questions from section $B$:$^5C_4 	imes ^5C_2 = 5 	imes 10 = 50$ ways.Total number of ways $= 50 + 100 + 50 = 200$.

$A$ question paper is divided into two parts,$A$ and $B$,each consisting of $5$ questions. If a candidate has to select $6$ questions in total,in how many ways can they do so if they must select at least $2$ questions from each part?

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